In the paper Uniform(0,1) Two-Person Poker Models the authors point out that, in the von Neumann model of the [0,1] game, the OOP player has a unique optimal strategy, and while the IP player has many optimal strategies, it has only one admissible strategy. They write,

“A strategy is admissible if no other strategy gives a better expected payoff against one strategy of the opponent without giving a worse expected payoff against another strategy of the opponent” (p. 1).

From this definition, I can’t tell the difference between weak domination and admissibility; can anybody else? Also, does anyone know of any proofs related to admissible strategies (e.g. that certain conditions guarantee the existence of a unique admissible strategy)?

Admissible strategy = not weakly dominated strategy

Weakly dominated is usually used in the context of pure strategies (some authors write 'weakly dominated action' to be clear), but admissible is usually used in the context of mixed strategies.

You can't hope for unique admissible strategies in general (imagine if the payoff matrix were entirely zero).

There are refinements of NE which guarantee admissibility (trembling hand perfect and quasi-perfect), and also linear programming algorithms which can construct admissible NE's.

Thanks marva, very informative.